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Chapter 8

Chapter 8. Section 3. Adding and Subtracting Radicals. Add and subtract radicals. Simplify radical sums and differences. Simplify more complicated radical expressions. 8.3. 2. 3. Objective 1. Add and subtract radicals. Slide 8.3-3.

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Chapter 8

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  1. Chapter 8 Section 3

  2. Adding and Subtracting Radicals Add and subtract radicals. Simplify radical sums and differences. Simplify more complicated radical expressions. 8.3 2 3

  3. Objective 1 Add and subtract radicals. Slide 8.3-3

  4. We add or subtract radicals by using the distributive property. For example, Only like radicals— those which are multiples of the same root of the same number— can be combined this way. The preceding example shows like radicals. By contrast, examples of unlike radicals are Radicands are different Indexes are different Note that cannot be simplified. Add and subtract radicals. Slide 8.3-4

  5. Add or subtract, as indicated. EXAMPLE 1 Adding and Subtracting Like Radicals Solution: It cannot be added by the distributive property. Slide 8.3-5

  6. Objective 2 Simplify radical sums and differences. Slide 8.3-6

  7. Sometimes, one or more radical expressions in a sum or difference must be simplified. Then, any like radicals that result can be added or subtracted. Simplify radical sums and differences. Slide 8.3-7

  8. Add or subtract, as indicated. EXAMPLE 2 Simplifying Radicals to Add or Subtract Solution: Slide 8.3-8

  9. Objective 3 Simplify more complicated radical expressions. Slide 8.3-9

  10. When simplifying more complicated radical expressions, recall the rules for order of operations from Section 1.2. A sum or difference of radicals can be simplified only if the radicals are like radicals. Thus, cannot be simplified further. Simplify more complicated radical expressions. Slide 8.3-10

  11. Simplify each radical expression. Assume that all variables represent nonnegative real numbers. EXAMPLE 3 Simplifying Radical Expressions Solution: Slide 8.3-11

  12. Simplify each radical expression. Assume that all variables represent nonnegative real numbers. EXAMPLE 3 Simplifying Radical Expressions (cont’d) Solution: Slide 8.3-12

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